ProtoDash: Fast Interpretable Prototype Selection

In this paper we propose an efficient algorithm ProtoDash for selecting prototypical examples from complex datasets. Our generalizes the learn to criticize (L2C) work by Kim et al. (2016) to not only select prototypes for a given sparsity level $m$ but also to associate non-negative (for interpretability) weights with each of them indicative of the importance of each prototype. This extension provides a single coherent framework under which both prototypes and criticisms can be found. Furthermore, our framework works for any symmetric positive definite kernel thus addressing one of the key open questions laid out in Kim et al. (2016). Our additional requirement of learning non-negative weights no longer maintains submodularity of the objective as in the previous work, however, we show that the problem is weakly submodular and derive approximation guarantees for our fast ProtoDash algorithm. We demonstrate the efficacy of our method on diverse domains such as retail, digit recognition (MNIST) and on publicly available 40 health questionnaires obtained from the Center for Disease Control (CDC) website maintained by the US Dept. of Health. We validate the results quantitatively as well as qualitatively based on expert feedback and recently published scientific studies on public health, thus showcasing the power of our method in providing actionability (for retail), utility (for MNIST) and insight (on CDC datasets), which presumably are the hallmark of an effective interpretable method.